<header>
    证明
</header>
<p>
    在平面坐标系中，有一个点
    <code>
    ["join",["rightTop","p","'"],"(",["rightTop","x","'"],",",["rightTop","y","'"],")"]
</code>
    经过逆时针旋转θ度，那么坐标变换公式就是：
</p>
<p>
    <code>
        ["equationSet",
            ["join","x=",["rightTop","x","'"],"cosθ - ",["rightTop","y","'"],"sinθ"],
            ["join","y=",["rightTop","x","'"],"sinθ + ",["rightTop","y","'"],"cosθ"]
        ]
    </code>
</p>
<h2>
    证：
</h2>
<img src="./images/rotate_x_y.jpeg" />
<p>
    由上图可得：
</p>
<p>
    <code>
        ["equationSet",
            ["join",["division","x","R"]," = cos(α + θ) = cosθcosα - sinθsinα"],
            ["join",["division","y","R"]," = sin(α + θ) = cosαsinθ + cosθsinα"]
        ]
    </code>
</p>
<p>
    进一步可得：
</p>
<p>
    <code>
        ["equationSet",
            ["join","x = Rcosθcosα - Rsinθsinα = Rcosα * cosθ - Rsinα * sinθ = ",["rightTop","x","'"],"cosθ - ",["rightTop","y","'"],"sinθ"],
            ["join","y = Rcosαsinθ + Rcosθsinα = Rcosα * sinθ + Rsinα * cosθ = ",["rightTop","x","'"],"sinθ + ",["rightTop","y","'"],"cosθ"]
        ]
    </code>
</p>
<p>
    至此，上述得证。
</p>